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Math Help - Maths B question

  1. #1
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    Maths B question

    The operators of the ferris wheel would like to inject some more excitement into their rides and would like to increase the number of revolutions per minute . Their experience tells them that nausea can occur when riders are subjected to vertical speed in excess of 1m/s. Assist them by using mathematics to estimate the number of revolutions per minute the ferris wheel can go before running the risk of riders being sick all over the place ?

    The wheels diameter is 20 metres and it takes 2 minutes to complete one counter-clockwise revolution. Rides last for three revolutions.
    I found the h(t)= 10sin(pi/60 t -pi/2)+10
    Apparently I can differentiate that to = 1/6 pi sin(pi/60 t)
    then make the differentaited equation = 1
    then i dont know the right answer for t because I keep getting different answers .
    even so what does this t value mean in terms of the whole question ?


    HELP PLEASE
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  2. #2
    Super Member
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    Re: Maths B question

    You can do this problem with just algebra. The vertical speed is greatest when the rider is to the side, and so they want the vertical speed to be 1 m/s there. The radius of the wheel is 10m - yeah, they tried to trick us by giving the diameter. The angular speed is then:

    1\ \frac{\text{m}}{\text{sec}}\ \frac{1\ \text{rev}}{2 \pi 10\ \text{m}}\ \frac{60\ \text{sec}}{1\ \text{min}} = \frac{3}{\pi},

    or approximately 0.955\ \frac{\text{rev}}{\text{min}}.

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